There is more to Rebecca's story than just the portion I have included here; you can find out more in the article in Wikipedia, and you can also read Genesis 26 and Genesis 27 for more details.
[Notes by LKG]
This story is part of the Bible Women unit. Story source: King James Bible (1611): Genesis 24 and Genesis 25 [LIBRIVOX AUDIO].
And he made his camels to kneel down without the city by a well of water at the time of the evening, even the time that women go out to draw water.
And he said, "O LORD God of my master Abraham, I pray thee, send me good speed this day, and shew kindness unto my master Abraham. Behold, I stand here by the well of water; and the daughters of the men of the city come out to draw water. And let it come to pass, that the damsel to whom I shall say, 'Let down thy pitcher, I pray thee, that I may drink;' and she shall say, 'Drink, and I will give thy camels drink also,' let the same be she that thou hast appointed for thy servant Isaac; and thereby shall I know that thou hast shewed kindness unto my master."
And it came to pass, before he had done speaking, that, behold, Rebekah came out, who was born to Bethuel, son of Milcah, the wife of Nahor, Abraham's brother, with her pitcher upon her shoulder. And the damsel was very fair to look upon, a virgin, neither had any man known her: and she went down to the well, and filled her pitcher, and came up.
And the servant ran to meet her, and said, "Let me, I pray thee, drink a little water of thy pitcher."
And she said, "Drink, my lord," and she hasted, and let down her pitcher upon her hand, and gave him drink.
And when she had done giving him drink, she said, "I will draw water for thy camels also, until they have done drinking." And she hasted, and emptied her pitcher into the trough, and ran again unto the well to draw water, and drew for all his camels.
And the man wondering at her held his peace, to wit whether the LORD had made his journey prosperous or not. And it came to pass, as the camels had done drinking, that the man took a golden earring of half a shekel weight, and two bracelets for her hands of ten shekels weight of gold; And said, "Whose daughter art thou? Tell me, I pray thee: is there room in thy father's house for us to lodge in?"
And she said unto him, "I am the daughter of Bethuel the son of Milcah, which she bare unto Nahor." She said moreover unto him, "We have both straw and provender enough, and room to lodge in."
And the man bowed down his head, and worshipped the LORD. And he said, "Blessed be the LORD God of my master Abraham, who hath not left destitute my master of his mercy and his truth: I being in the way, the LORD led me to the house of my master's brethren."
And the damsel ran, and told them of her mother's house these things.
And Rebekah had a brother, and his name was Laban: and Laban ran out unto the man, unto the well.
And it came to pass, when he saw the earring and bracelets upon his sister's hands, and when he heard the words of Rebekah his sister, saying, "Thus spake the man unto me;" that he came unto the man; and, behold, he stood by the camels at the well.
And he said, "Come in, thou blessed of the LORD; wherefore standest thou without? for I have prepared the house, and room for the camels."
And they called Rebekah, and said unto her, "Wilt thou go with this man?"
And she said, "I will go."
And they sent away Rebekah their sister, and her nurse, and Abraham's servant, and his men. And they blessed Rebekah, and said unto her, "Thou art our sister, be thou the mother of thousands of millions, and let thy seed possess the gate of those which hate them."
And Rebekah arose, and her damsels, and they rode upon the camels, and followed the man: and the servant took Rebekah, and went his way.
And Isaac came from the way of the well Lahai-roi; for he dwelt in the south country.
And Isaac went out to meditate in the field at the eventide: and he lifted up his eyes, and saw, and, behold, the camels were coming.
And Rebekah lifted up her eyes, and when she saw Isaac, she lighted off the camel.
For she had said unto the servant, "What man is this that walketh in the field to meet us?"
And the servant had said, "It is my master;" therefore she took a vail, and covered herself.
And the servant told Isaac all things that he had done.
And Isaac brought her into his mother Sarah's tent, and took Rebekah, and she became his wife; and he loved her: and Isaac was comforted after his mother's death.
And Isaac was forty years old when he took Rebekah to wife, the daughter of Bethuel the Syrian of Padan-aram, the sister to Laban the Syrian.
And Isaac intreated the LORD for his wife, because she was barren: and the LORD was intreated of him, and Rebekah his wife conceived.
And the children struggled together within her; and she said, "If it be so, why am I thus?" And she went to inquire of the LORD.
And the LORD said unto her, "Two nations are in thy womb, and two manner of people shall be separated from thy bowels; and the one people shall be stronger than the other people; and the elder shall serve the younger."
And when her days to be delivered were fulfilled, behold, there were twins in her womb. And the first came out red, all over like an hairy garment; and they called his name Esau.
And after that came his brother out, and his hand took hold on Esau's heel; and his name was called Jacob: and Isaac was threescore years old when she bare them.
And the boys grew: and Esau was a cunning hunter, a man of the field; and Jacob was a plain man, dwelling in tents.
And Isaac loved Esau, because he did eat of his venison: but Rebekah loved Jacob.